My money wouldn't be on your S3. In fact, it would never even have been considered an option. Unless YOU have 60 BHP more, and bigger nuts to boot, then I would maybe give it consideration.
Scoobies are thoroughbred racing machines. A3's are everyday hatchbacks. No amount of tinkering is going to get even equal power machines to act the "same" in a race.
If you want to beat your mate, get a faster scooby or evo. Little else for similar coin will even come close. You just need to watch top gear where Clarkson follows the lambo round the track in the evo to realise these rally based machines are seriously quick. Your A3 aint keeping up for love nor money. Well, unless your rocking 450 BHP and there aint corners.